The invention is based on a fuel injection system of the general type described hereafter. A fuel injection system having a pressure sensor in the intake tube is already known; in this system, a pneumatic damping apparatus is provided in the intake tube pressure sensor in order to prevent errors in measurement caused by periodic pressure fluctuations in the intake tube of the internal combustion engine. However, this system has the disadvantage that a damping apparatus of this kind acts over the entire operating range of the engine, so that particularly in the partial-load range of the engine, pressure changes are detected by the intake tube pressure sensor only in a delayed manner.